The Influence of a Submarine Canyon on the Circulation and Cross-Shore

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The Inﬂuence of a Submarine Canyon on the Circulation and Cross-Shore Exchanges around an Upwelling Front

GONZALO S. SALDÍAS Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, British Columbia, Canada, and Departamento de Fı´sica, Facultad de Ciencias, Universidad del Bı´o-Bı´o, Concepción, and Centro FONDAP de Investigación en Dinámica de Ecosistemas Marinos de Altas Latitudes, Valdivia, Chile

SUSAN E. ALLEN Department of Earth, Ocean and Atmospheric Sciences, University of British Columbia, Vancouver, British Columbia, Canada

(Manuscript received 23 May 2019, in ﬁnal form 17 March 2020)

ABSTRACT

The response of a coastal ocean numerical model, typical of eastern boundaries, is investigated under upwelling-favorable wind forcing and with/without the presence of a submarine canyon. Experiments were run over three contrasting shelf depth/slope bathymetries and forced by an upwelling-favorable alongshore wind. Random noise in the wind stress field was used to trigger the onset of frontal instabilities, which formed around the upwelling front. Their development and evolution are enhanced over deeper (and less inclined) shelves. Experiments without a submarine canyon agree well with previous studies of upwelling frontal instabilities; baroclinic instabilities grow along the front in time. The addition of a submarine canyon incising the continental shelf dramatically changes the circulation and frontal characteristics. Intensified upwelling is channeled through the downstream side of the canyon in all depth/slope configurations. Farther downstream a downwelling area is generated, being larger and stronger on a shallow shelf. The canyon affects mainly the location of the southward upwelling jet, which is deflected inshore and accelerated after passing over the canyon. This process is accompanied by a break in the alongshore scale of the instabilities on either side of the canyon. Term balances of the depth-averaged cross-shore momentum equation reaffirm the downstream acceleration of the jet and the increased wavelength of the instabilities, and clarify the dominant balance between the advection and ageostrophic terms around the canyon.

1. Introduction the surface forming a density front (upwelling front) separating relatively warm waters offshore from cold Dominant equatorward upwelling-favorable winds drive upwelling waters next to the coastal boundary (Brink coastal upwelling along major eastern boundary systems 1983). The lateral density gradients around the front during spring–summer (e.g., Nelson and Hutchings 1983; sustain the development and evolution of a geostroph- Allen et al. 1995; Letelier et al. 2009; Barton et al. 2013). ically balanced upwelling jet that flows downstream with This wind forcing promotes the offshore transport of 2 core velocities ;0.5 m s 1 (e.g., O’Brien and Hurlburt water in the surface Ekman layer, with a compensating 1972; Kosro et al. 1997; Castelao and Barth 2007). This onshore flow at depth that brings cold, salty (and high process is also characterized by low (high) sea level density), nutrient-rich, and oxygen-poor water over the nearshore (offshore) (e.g., Whitney and Allen 2009a), shelf (Brink 1983; Huyer 1983). The rise of these sub- and the formation of prominent frontal instabilities in surface waters to the euphotic zone supports a large the form of filaments around the front (Flament et al. fraction of biological production and fisheries in these 1985; Washburn and Armi 1988; Barth 1989; Durski and relatively small coastal areas (e.g., Carr and Kearns Allen 2005; Troupin et al. 2012). 2003). Upwelled waters over the shelf eventually reach The presence of a submarine canyon breaks the con- tinuity of the along-isobath geostrophic flow (Allen and Corresponding author: Gonzalo S. Saldías, [email protected] Durrieu de Madron 2009), which leads to cross-isobath

DOI: 10.1175/JPO-D-19-0130.1 Ó 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 10/07/21 03:05 PM UTC 1678 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 50

flow and exchange of water and tracers between the topography using s coordinates (Dawe and Allen 2010). open ocean and the continental shelf (Hickey 1995; The horizontal pressure gradient is treated with a spline Alvarez et al. 1996; Skliris et al. 2001; Allen 2004; Allen density Jacobian (Shchepetkin and McWilliams 2003). and Hickey 2010; Ramos-Musalem and Allen 2019). As Vertical mixing follows the Mellor–Yamada level 2.5 submarine canyons represent locations of increased closure scheme (Mellor and Yamada 1982); the back- 2 ageostrophic circulation, their impacts on cross-shelf ground vertical viscosity and diffusivity are 1 3 10 5 and 2 2 exchanges are potentially large at regional scales 5 3 10 6 m2 s 1, respectively. Bottom stress is calculated (Connolly and Hickey 2014; Brink 2016b). In general, with a quadratic drag law using a bottom roughness of 2 several studies have analyzed the circulation within 2 3 10 2 m. ROMS has been used in several studies of submarine canyons (e.g., Klinck 1996; Flexas et al. 2008; flow over topography, including submarine canyons Allen and Hickey 2010), however, the influence of (e.g., She and Klinck 2000; Dinniman and Klinck 2002; canyon-associated circulation on surrounding shelf wa- Rennie et al. 2009; Chen et al. 2014; Connolly and ters has received less attention (e.g., Hickey 1998; Chen Hickey 2014) and banks (e.g., Kim et al. 2009; Whitney and Allen 1996). and Allen 2009a,b), and in studies of frontal instabil- Cross-shelf exchanges can be significantly enhanced ities (e.g., Durski and Allen 2005; Capetetal.2008; not only by the presence of a major bathymetric barrier Brink 2016a). as a submarine canyon (Allen and Durrieu de Madron The model domain is a rectangular basin resembling 2009), but also due to the high vorticity field created by the coastal ocean of an eastern boundary margin with frontal instabilities (Durski and Allen 2005; Wang and 155 and 600 km in the cross-shore and alongshore di- Jordi 2011). Although shelf-slope exchanges have been rection, respectively (Fig. 1). Grid spacing increases widely studied and reviewed (e.g., Houghton et al. 1988; beyond x 5250 km in the cross-shore direction for Huthnance 1995; Dinniman and Klinck 2004; Brink computational efficiency from 0.5 km nearshore to 10 km 2016a), there is scarce information on the combined at the offshore boundary, whereas a fixed 0.5 km of grid effect and/or the interaction between surface frontal spacing is set in the alongshore direction and in the instabilities and a submarine canyon. A few studies have nearshore region (x , 50 km) (Fig. 1b). Different shelf considered the case of mesoscale instabilities over a slope configurations are tested with all cases having a submarine canyon under right bounded flow conditions maximum depth of 500 m in the open ocean. We started (typical of downwelling alongshore currents; Jordi et al. with a basic configuration in order to compare with pre- 2005, 2008), and thus, the effect of a submarine canyon vious (and well recognized results) of upwelling over a over the circulation and characteristics of an upwelling canyon cutting across a deep flat shelf (Klinck 1996)—our front remains poorly understood. The aim of this study is basic experiments are run with the same shelf and canyon to clarify this canyon effect and to quantify its impact on topography, which is defined by cross-shore exchanges for a typical eastern boundary upwelling system. Section 2 presents the details of the H 2x 2 x (y) H(x, y) 5 H 2 s 1 2 tanh o , (1) model configuration and experiments, section 3 contains m 2 a the main results, the discussion is presented in section 4, and finally the conclusions are highlighted in section 5. where Hm is the maximum depth of the domain (500 m), Hs is the depth change from the continental shelf to the open ocean (400 m), a is the transition scale defining 2. Model configuration and experiments the slope of the cross-shelf profile (5 km), and xo(y) is the The Regional Ocean Modeling System (ROMS) is location of the shelf break, defined as used in this study. ROMS is a primitive equation model formulated in finite-difference form with a sigma- 2(y2 2 y2) x (y) 5 x 1 x 1 2 exp o , (2) coordinate representation in the vertical direction that o n b 2b2 solves the hydrostatic nonlinear primitive equations

(Haidvogel et al. 2000; Shchepetkin and McWilliams where xn is the nominal distance of the head of the 2005). Vertical differencing is achieved with terrain- canyon from the coastal wall (12 km), xb is the distance following s coordinates (Song and Haidvogel 1994). In added to xn to reach the shelf break (10 km), yo is the this study, the model is run with a third-order upstream location of the center of the canyon (at y 5 0 km), and horizontal and a fourth-order centered vertical advec- b is the width scale of the canyon (2.5 km). This config- tion scheme for momentum and tracers. High-order uration produces a canyon ;10 km wide in its mouth, advection is necessary to avoid spurious vertical veloc- 20 km long from its mouth to the head, and with sidewall ities at the canyon rim due to stratified flow over steep steepness of ;0.065 (Figs. 2a,d). We also run a series of

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FIG. 1. (a) Model domain bathymetry (colors; m) with the location of the submarine canyon enclosed in a gray box and (c) shown expanded. (b) Cross-shore grid spacing—minimum grid spacing is 500 m nearshore in the x direction and increasing offshore of 50 km. The grid spacing in the y direction is constant (500 m) along the whole domain. The 150, 200, 300, and 400 m isobaths are shown in magenta contours in (c). experiments with more realistic sloping shelves (Figs. 2b,c) All runs are forced only with a horizontally uniform by changing some key parameters in (1) and (2) (see surface wind stress that is ramped up from 0 to 2 Table 1). Vertical resolution is supplied by 30 s-coordinate 20.03 N m 2 in5days(fromday10to15),afterwhich levels with increased resolution near the surface and bot- it is maintained constant. We set the first 10 days of the tom in order to resolve the surface and bottom boundary model to run free in order to let transients decay. layers. The domain has three open boundaries (north, Initial conditions in temperature and salinity are set south, and offshore). Free-slip conditions are applied along horizontally uniform and taken from the average profiles the coast. On the three open boundaries, implicit gravity from all spring–summer glider observations off Oregon wave radiation conditions (Chapman 1985) are applied during the period 2006–14. Thus, our density and strati- to the surface elevation, whereas the Flather radiation fication conditions are similar to previous studies of scheme (Flather 1976) is applied for depth-averaged hor- coastal upwelling instabilities off Oregon (Durski and izontal velocities. Orlanski radiation conditions (Orlanski Allen 2005). 1976) are applied to the baroclinic velocities, temperature, and salinity along the offshore boundary. A local two- 3. Results dimensional model is run in the northern and southern a. Coastal upwelling: No-canyon versus canyon cases boundary to obtain the local boundary conditions, as in other studies of coastal upwelling (Gan and Allen 2005; Coastal upwelling structure in a domain with along- Castelao and Barth 2007). shore uniform bathymetry shows key differences as

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FIG. 2. (a)–(c) Cross-shore depth profiles for the three bathymetry configurations (Table 1); solid and dashed gray lines correspond to the (d)–(f) along-canyon and ambient shelf profiles, respectively. The 150, 200, 300, and 400 m isobaths are also shown in magenta contours in (d)–(f). function of shelf slope (Figs. 3a–c). After 10 days of Depth-averaged vertical velocity fields are shown in upwelling-favorable winds, frontal instabilities are en- Fig. 4. Stripes of upward and downward flow are evident hanced over deeper (and less inclined) continental along the upwelling front and are fairly consistent with shelves (Figs. 3a,b). The surface circulation (as repre- patterns of divergence and convergence of the hori- sented by the streamlines in white) is primarily south- zontal velocity vectors (Figs. 4a–c). The presence of a westward in response to wind-driven upwelling for the submarine canyon enhances upwelling and downwelling three shelf configurations, however, the shallow shelf in the area around the canyon (Figs. 4d–f). In all case (Fig. 3c) presents less offshore-onshore fluctuations three canyon cases, strong upwelling is found within the as compared to its deeper shelf counterparts (Figs. 3a,b). canyon and on the downstream side over the shelf The presence of a submarine canyon considerably mod- (Figs. 4d–f). A region of strong downwelling is also lo- ifies the circulation and coastal upwelling structure in all cated farther south and is less pronounced in the deep cases; denser upwelling water is brought to the surface on shelf case (Figs. 4d–f). the downstream side of the canyon (primarily for the in- b. Cross-shore and alongshore upwelling structure termediate and shallow shelf cases; Figs. 3e,f), and the surface circulation meanders over the canyons (Figs. 3d–f). The vertical structure of coastal upwelling (as seen Frontal instabilities seem to have a longer alongshore through the velocity and density fields at day 25) differs scale, especially downstream of the canyon (Figs. 3d–f). considerably when a submarine canyon incises the

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S continental shelf (Fig. 5 versus Fig. 6). Minor differences occur upstream (y 5 15 km) of the canyon where upwelled isopycnals rise from about 50–70 m to the

Bu surface to form the upwelling front and jet (Figs. 5a–c). These differences represent some key upwelling features of the impact of a submarine canyon on the up- is the vertical aspect oc L / R stream circulation. Here, the upwelling jet is weaker for s

H the cases with a submarine canyon (Figs. 6a–c), and a bottom countercurrent (northward ﬂow) is formed near the coastal wall in the deep shelf experiment (Fig. 6a), o which is not well developed in the no-canyon case (Fig. 5a). The vertical structure of frontal instabilities is evident in the cross-shore velocity ﬁelds and is enhanced LR /

s over deeper shelves with an approximate vertical scale H of 50–60 m (Fig. 5d versus Fig. 5f). Some frontal instabilities form in the shallow shelf case with a canyon,

m) which are not clearly seen in the basic case without a 3 b

10 canyon (Fig. 6f versus Fig. 5f). 3 ( As expected, the presence of a submarine canyon changes dramatically the circulation and upwelling

m) structure in its vicinity: (i) the upwelling jet weakens in 3 a

10 all shelf cases (Figs. 6g–i versus Figs. 5g–i) and its ver- 3 . ( tical structure is partially fractured due to the cyclonic turn onshore, which is best seen in the deep shelf case

m) (Fig. 6g versus Fig. 5g), (ii) The cross-shore ﬂow is pre- 3 b x 10 dominantly onshore with stronger upwelling currents at 3 ( about the rim depth (Figs. 6j–l), and (iii) deep water (150–170 m) is transported up and onshore through the

m) canyon, and reaches the nearshore region on the shelf 3 n x Howatt and Allen (2013) 10 (Figs. 6j–l; black contours). After the jet passes over the 3 ) numbers are calculated using the canyon width at the shelf break and the shelf slope, respectively. ( S and canyon it moves onshore and accelerates (Figs. 6m–o are the Rossby numbers based on the length of the canyon (or width of the continental shelf) and the radius of versus Fig. 5m–o). As seen from the depth-averaged oc s R vertical velocity ﬁelds (Figs. 4d–f), more upwelling oc- H (m)

and curs nearshore over the shelf but strong downward ve- o

R locities dominate in an area farther downstream in the m H (m) continental shelf (Figs. 4d–f), which is characterized vertically by a tongue of offshore ﬂow extending down to )

2 the shelf break (Figs. 6p–r versus Figs. 5p–r). Allen and Hickey (2010) j 2 y t 0.03 500 400 12 10 5 2.5 — 0.03–0.05 — — 0 0.03 500 400 12 10 5 2.5 0.01 0.04–0.07 0.1–0.15 0.87 0 0.03 500 446 12 10 10 2.5 — 0.04–0.07 — — 0.30 0.03 500 446 12 10 10 2.5 0.009 0.04–0.06 0.1–0.14 0.82 0.30 0.03 500 486.5 12 10 10 2.5 — 0.03–0.06 — — 0.31 0.03 500 486.5 12 10 10 2.5 0.005 0.04–0.06 0.1–0.13 0.47 0.31

j Alongshore sections of density and cross-shore ﬂow 2 2 2 2 2 2 (N m along the upwelling jet show impacts of the canyon in upwelling structure, cross-shore exchanges, and the vertical structure of the frontal instabilities (Fig. 7). The canyon increases, to a large extent, the presence of upwelled denser waters along the downstream side of the canyon (Figs. 7d–f versus Figs. 7a–c). This enhanced upwelling is also characterized by the stretching of water parcels inside the canyon, which is consistent with the onshore turning of the ﬂow (Figs. 7j–l). The presence of a submarine canyon also changes the vertical struc-

1. List of experiments of upwelling circulation with and without a submarine canyon and under contrasting continental shelf conﬁguration. The term ture of the frontal instabilities. They are fairly well or- ganized in an offshore/onshore ﬂow pattern extending

ABLE through most of the water column (Figs. 7g–i). The up- T Expt Canyon Shelf curvature, respectively. Finally, theNondimensional numbers Burger are (Bu) computed and following topographic Burger ( Exp1 No Deep shelf ratio (depth of the shelf break over the canyon length), whereas Exp2 Yes Deep shelf Exp3 No Intermediate shelf Exp4 Yes Intermediate shelf Exp5 No Shallow shelf Exp6 Yes Shallow shelf stream characteristics do not change signiﬁcantly when a

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FIG. 3. Upwelling filaments as seen in surface potential density fields (in color) for (a)–(c) no-canyon and (d)–(f) canyon experiments with contrasting continental shelves at day 25. The isobaths of 150, 200, 300, and 400 m are shown in orange contours, whereas the surface circulation is illustrated with white streamlines for each case. Horizontal gray lines denote the location of cross-shore sections shown in Figs. 5 and 6. Surface flow is offshore and downwind, consistent with Ekman theory. Instabilities occur on the upwelling jet and are significantly impacted by the presence of a canyon. canyon is introduced into the system, however, the flow on alongshore scales, a wavelet power spectrum (WPS) is the downstream side is dramatically modified; the onshore shown for the days 21 and 25 along the same sections at upwelling flow over the canyon can extend up to the sur- x 528 and 210 km (Fig. 8, center and right panels). We face, and downwelling/offshore currents dominate down- followed the widely used code by Torrence and Compo stream around 10–30 km south of the canyon (Figs. 7j–l). (1998) with the power spectra rectified as in Liu et al. (2007). Short wavelengths of about 8–12 km dominate c. Characteristics of frontal instabilities and energetics during day 21 (Figs. 8b,h). The growth into larger The phase of the frontal disturbance propagates wavelengths is observed by day 25 with a wider range of southward in the direction of the mean flow as shown by alongshore scales from 8 to about 28 km (Figs. 8c,i). The the depth-averaged cross-shore velocity along the core influence of a submarine canyon is primarily evidenced of the jet between 8 and 10 km offshore (Fig. 8, left by the difference of dominant alongshore scales on the panels). The small-scale patterns that appear to domi- two sides of the canyon, and also by the intrusion of nate at the onset of the frontal instability grow to larger longer scales around the canyon in association with wavelengths during the last 3–4 days of the runs (see the background canyon circulation. Frontal instabilities Figs. 8a,g). To quantify these changes of the dominant are characterized by similar features (as no-canyon

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FIG. 4. Upwelling and downwelling regions as seen in depth-averaged vertical velocity fields (in color) for (a)–(c) no-canyon and (d)–(f) canyon experiments with contrasting continental shelves at day 25. The isobaths of 150, 200, 300, and 400 m are shown in red contours. The depth- averaged horizontal velocity field is shown in black vectors. Horizontal gray lines denote the location of cross-shore sections shown in Figs. 5 and 6. Note the locations of the core of the upwelling jet is about x 528 km for the deep and intermediate shelf, and at about x 5210 km for the shallow shelf. These locations are used in Figs. 7 and 8. Depth-averaged velocity shows onshore/offshore flow due to both the instabilities and the canyon, and clearly shows the impact of the canyon on strengthening the instabilities downstream of the canyon. experiments) on the upstream side but are considerably respectively. It is important to emphasize that the larger on the downstream side (;20–30 km; Figs. 8f,l). perturbation calculation is with respect to the along- Perturbation fields are decomposed, similar to other shore average and not the time average as in other studies (e.g., Durski and Allen 2005; Brink 2016a), to studies (Kang and Curchitser 2015). Thus, the near analyze the evolution of the perturbation vorticity field steady response to the canyon appears primarily in and the conversion of energy, as follows: the eddy terms for the downstream region as it is shown later in the energetics. The alongshore scale is q(x, y, z, t) 5 q 1 q0 , (3) defined here as Ly, which is the distance from an ini- ð L tial Li to final Lf alongshore extension of the model 1 f q(x, z, t) 5 qdy, (4) domain. Thus, the perturbation vorticity field is cal- L y Li culated as 0 0 r y 0 ›y ›u where q is the density or a velocity component ( , u, ,or z 5 2 . (5) w), q and q0 are its alongshore average and perturbation, ›x ›y

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FIG. 5. Cross-shore sections of the velocity (colors) and density (red and black contours) ﬁelds at (a)–(f) y 5 15 km, (g)–(l) y 5 0 km, and (m)–(r) y 5215 km showing the structure of coastal upwelling for the three bathymetry conﬁgurations without a submarine canyon (Exp1, Exp3, and Exp5) at day 25.

The evolution of the surface z0 ﬁeld adds additional for the deep shelf experiments, and these instabilities insights about the formation of frontal instabilities and are characterized by tilting downstream and offshore the inﬂuence of a submarine canyon on their evolution (Fig. 9b). The presence of the canyon disrupts their early (Fig. 9) as compared to previous studies without the development downstream and increases the anticyclonic presence of a canyon (Durski and Allen 2005). The perturbation vorticity over this region (Fig. 9f). By day generation of the instabilities is clearly seen by day 18 20 the instabilities have already curved backward on

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FIG. 6. Cross-shore sections of the velocity (colors) and density (red and black contours) field at (a)–(f) y 5 15 km, (g)–(l) y 5 0 km, and (m)–(r) y 5215 km showing the structure of coastal upwelling for the three bathymetry configurations with a submarine canyon (Exp2, Exp4, and Exp6) at day 25. their offshore side (Figs. 9c,g), and have formed down- instabilities with characteristic long stripes of positive stream of the canyon. However, they have greater vorticity. The submarine canyon impacts the charac- alongshore separations (i.e., wavelength) than those teristics of the instabilities by increasing their along- located north of the canyon (Fig. 9g), as was already shore scale and promoting a region of negative vorticity shown by the WPS. By day 25 the upper ocean of next to the canyon (downstream side; Figs. 9h,p versus the continental shelf is completely influenced by the Figs. 9d,l). Key differences are also identified in the

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FIG. 7. Alongshore sections of (a)–(f) potential density and (g)–(l) cross-shore velocity fields along the core of the upwelling jet (at x 528 and 210 km), showing the density structure and cross-shore exchanges for all experiments at day 25. Positive cross-shore velocities in (g)–(l) mean onshore flow. shallow shelf cases with respect to the former deep shelf to eddy kinetic energy (KmKe), and the energy reservoirs description. The formation of the surface instabilities (MPE, EPE, MKE, and EKE) are calculated as ð ð takes longer (Figs. 9i–l), and the influence of the sub- X 0 5 2 r marine canyon has a greater impact not only over the PmKm g a wdzdx, (6) 2 downstream side but also on the upstream side where 0 H ð ð bands of positive and negative perturbation vorticity X 0 g2 ›r ›r PmPe 5 2 a u0r0 1 a w0r0 dz dx, are generated earlier as seen by day 15 (Fig. 9m). The r 2 › a › a 0 2H N x z formation of the instabilities by day 20 also differs con- o (7) siderably over the upstream region since enhanced nega- ð ð tive vorticity bands are only found when there is a canyon X 0 5 2 0r0 in the shallow shelf case (Fig. 9o versus Fig. 9k). Finally, PeKe gw a dz dx, (8) 0 2H the downstream cyclonic/anticyclonic vorticity areas are ð ð formed early during the ramp-up time (days 10–15). Note X 0 ›y ›y ›u KmKe 5 2 r u0y0 1 w0y0 1 u0u0 o › › › that the marked band of cyclonic vorticity delimits the 0 2H x z x region of intense downstream upwelling (see Fig. 3f). ›u 1 w0u0 dz dx, (9) The conversion of energy provides clarifying informa- ›z tiononthesourceofenergyandthetypeofinstabilities ð ð X 0 g2r 2 being developed. Following Kang and Curchitser (2015), 5 a MPE 2 dz dx, (10) 2 2r N the conversions of (i) mean potential energy to mean ki- 0 H o netic energy (PmKm), (ii) mean potential energy to eddy ð ð X 0 g2r02 potential energy (PmPe), (iii) eddy potential energy to EPE 5 a dz dx, (11) r 2 eddy kinetic energy (PeKe), and (iv) mean kinetic energy 0 2H 2 oN

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FIG. 8. Evolution of cross-shore exchanges as seen in (left) Hovmoller diagrams of depth-averaged cross-shore velocities along the core of the upwelling jet. Quantification of dominant alongshore scales of variability from a wavelet power spectrum (WPS) of depth-averaged cross-shore velocities (from the left panels) at times (center) 21 and (right) 25 days. The color of the WPS is the base 2 logarithm of power 2 spectral density (m2 s 2; scale at top). Enclosed light blue areas in the WPS denote dominant wavelengths along the upwelling front (95% significance). Shaded gray regions at the bottom of each panel indicate the cone of influence where edge effects become important. The instability shows increased wavelengths downstream of the canyon. ð ð X 0 1 r 5 r 2 1 y2 Here r is the density field from the initial conditions and MKE o(u ) dz dx, and (12) 0 2H 2 X 5230 km is the offshore extension of the integrals. ð ð X 0 1 Once the wind is turned on there is available mean EKE 5 r (u02 1 y02) dz dx, (13) o kinetic energy to be converted to mean potential energy 0 2H 2 that is evident from the increasing negative PmKm term where ra is the perturbation density calculated as the total den- (Fig. 10, left panels). Consequently, there is a persistent sity minus a reference density [ra(x,y,z,t)5 r(x,y,z,t)2 rr(z)]. gain of MPE (larger on the downstream side) (Fig. 10,

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FIG. 9. Evolution of surface (for the first sigma level) perturbation vorticity field [Eq. (5)] normalized by f for deep shelf (DS) and shallow shelf (SS) experiments. The isobaths of 150, 200, 300, and 400 m are shown in black contours. The presence of a submarine canyon produces areas with contrasting vorticity, especially in the SS case. right panels). The conversions of energy are similar for than the MKE reservoir (Figs. 10b,d). The shallow the deep and intermediate shelf cases, with the excep- shelf case differs considerably from the previous two tion of a larger fluctuation in PmPe (even turning neg- bathymetric configurations in that the PmPe conver- ative; with conversion from EPE to MPE) during days sion is persistently negative (conversion from EPE to 22 and 23 (Fig. 10c). All conversions to eddy potential MPE) and starts early in the simulation (about day 14; and eddy kinetic energy start about day 17–18 when the Fig. 10e). Thus, there is a massive gain of MPE as a frontal instabilities start to form. In both cases there is an consequence of the canyon circulation before the start of increase of EPE on the downstream side but is lower the development of frontal instabilities, and the EPE

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FIG. 10. (left) Energy conversions and (right) energy reservoirs for (a),(b) deep shelf, (c),(d) intermediate shelf, and (e),(f) shallow shelf experiments with a submarine canyon. The energetics have been separated for upstream (20 , y , 200) and downstream (2200 km , y ,220 km) regions in each case. becomes larger than the MKE (Fig. 10f). The evolution 18 to the end of the runs (Figs. 11a,e,i,m), which is of PeKe and KmKe for deep shelf and shallow shelf consistent with the evolution of baroclinic instabilities. cases are presented in Fig. 11 as function of cross-shore Although positive values of KmKe suggest some partial direction and time (integration only by depth through contribution of mean to eddy kinetic energy in the deep the upper half of the water column) to further visualize shelf experiment without a canyon (Figs. 11b,f), their details of the conversions to EKE, which are the smallest magnitudes are considerably lower than PeKe values at conversion terms in Fig. 10. These calculations are pre- the same time and cross-shore position. The presence sented for the upper half of the water column, and in a of a submarine canyon does not change the dominance smaller area on either side of the canyon, in order clarify of PeKe (i.e., baroclinic instabilities) on either side of these conversion terms in the upper ocean where the the canyon (Figs. 11c,g), however, more negative KmKe instabilities are more intensiﬁed. For no-canyon cases, values on the downstream region (Fig. 11h) are consis- both deep and shallow shelf (DS and SS, respectively) tent with the acceleration of the mean ﬂow after passing experiments reveal a dominant conversion from eddy over the canyon (there is conversion from eddy to mean potential to eddy kinetic energy (PeKe) from about day kinetic energy). In contrast with the energetics in the

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FIG. 11. Evolution of PeKe and KmKe for experiments with (Exp2 and Exp6) and without (Exp1 and Exp5) a submarine canyon for deep shelf (DS) and shallow shelf (SS) experiments. The quantification of PeKe and KmKe has been separated for upstream (10 km , y , 40 km) and downstream (240 km , y ,210 km) regions near the canyon in each case. The presence of a canyon modifies the energetics on the continental shelf, mainly downstream of the canyon in the SS case. deep shelf canyon case, the presence of a canyon positive perturbation vorticity (Figs. 9m–p); there is a changes considerably the conversion of energy on the gain of eddy potential energy and an acceleration of the downstream region of the shallow shelf experiment mean flow. (Figs. 11o,p). Here, the generation of baroclinic insta- d. Cross-shore transports along the upwelling jet bilities occurs only after day 21 and is restricted to the offshore side of the front (Fig. 11o). The main axis of Considering that both frontal instabilities and a sub- negative PeKe and KmKe (Figs. 11o,p) agrees well with marine canyon induce intensified cross-shore exchanges, the offshore limit of intensified upwelling (Fig. 3f) and the quantification of the transports with and without a

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FIG. 12. (a)–(d) Cross-shore (CS) and cumulative transports through the meridional planes shown in Fig. 7 as a function of time, and (e),(f) CS transports as function of meridional distance (230 , y , 30) through the 25 days of runs. The transports are color coded for deep shelf (red curves), intermediate shelf (blue curves), and shallow shelf (black curves) experiments. Note the differences in scales between the left and right panels. Onshore transport is greatly enhanced in deepest shelves with a submarine canyon. submarine canyon provides elucidating results on the low sea level nearshore (Fig. 12a). The development of competition of both effects on the net cross-shore ﬂow frontal instabilities after about day 19 causes oscillations under steady wind forcing (Fig. 12). When no-canyon is in the amount of water being transported offshore, and introduced in the system, the transport is mainly off- even occasional net onshore transport by the end of the shore in response to wind-driven coastal upwelling with deep and intermediate shelf experiments (Fig. 12a).

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Overall, these fluctuations do not change the general Our canyon experiments show all these aspects of the trend of an increasing accumulated offshore transport circulation associated with a canyon. Moreover, they along the upwelling jet over time, and with an increased add further insights about the circulation associated volume of water transported offshore in cases with with the interaction of a canyon with the upwelling jet deeper shelves (Fig. 12b). Thus, there is the expected net and its frontal instabilities; canyon-associated currents export of shelf water to the open ocean due to Ekman can eventually influence the entire water column (even transport and low sea level nearshore. The presence of a reaching up to the surface). Here, the strong flow of the submarine canyon modifies this pattern completely. As upwelling jet is deflected onshore and accelerated after seen in Figs. 7j–l, a submarine canyon generates intense passing the main canyon axis. This study confirms that, onshore flow primarily on its downstream side, which in the absence of a major bathymetric constraint such can be spread throughout the whole water column. This as a submarine canyon, baroclinic (the potential energy results in massive onshore transport of deep/offshore field is the primary source of perturbation kinetic energy) water onto the continental shelf (Figs. 12b,d). The shelf frontal instabilities are formed along an eastern boundary slope/depth has, again, a large control on the amount of upwelling front as previous studies have shown (Barth water being transported onshore, with deeper shelves 1989; Durski and Allen 2005; Capet et al. 2008). The in- having larger transports. The shallow shelf configuration fluence of a canyon does not significantly perturb the result has a significant drop of the transport after day 15 characteristics of frontal instabilities upstream of the (Fig. 12c). This is the result of the more intense down- canyon as evidenced by the evolution of characteristic welling circulation created over the downstream side of wavelengths and PeKe in cases with and without a the canyon (see Fig. 4f). However, this is not enough to canyon. Even though dominant wavelengths do grow in overcome the net onshore pattern on a regional scale. time, these would not be associated with a wave–wave Additional calculations using an extended alongshore interaction, as previously seen in Durski and Allen scale (200 km) reduces considerably the impact of the (2005), since the evolution of PeKe is always greater canyon promoting enhanced onshore transport (not than KmKe in our noncanyon experiments. This dif- shown). The alongshore variation of the onshore trans- ference might be because of the relatively short period port does not reveal regions with opposing trends when of steady winds (10 days) in our experiments compared only frontal instabilities are considered—cross-shore to the cases of Durski and Allen (2005). Our results, transport presents alongshore fluctuations (largest for however, show completely new findings regarding the a deeper shelf) but it has a net offshore component development and evolution of frontal instabilities over a (Fig. 12e). The canyon cases, on the other hand, are canyon due to its unique coastal upwelling setting along an characterized by dissimilar regions of persistent onshore eastern boundary. Previous studies have confirmed a sig- and offshore transports. The largest onshore flow is nificant increase of cross-shore and vertical motions by the concentrated around the downstream half of the canyon effects of the interaction of an unstable meander with a (Fig. 12f), whereas a net offshore transport occurs far- submarine canyon (Jordi et al. 2006, 2008). Nonetheless, ther downstream (230 , y ,25 km). Another up- their configuration corresponded to a coastal front typical welling region is generated south of ;225 km but only of buoyancy-driven currents (isopycnals tilting upward for the shallow shelf run (Fig. 12f). in the offshore direction). Recently, the presence of arrested coastal trapped waves (CTW) on the downstream side of a shallow valley has been suggested as a 4. Discussion dominant mechanism for the meander scale after the From previous studies, the general impacts of a sub- flow passes the valley (Zhang and Lentz 2017). This marine canyon cutting across the continental shelf on phenomenon occurs when a CTW phase speed matches the coastal circulation and exchanges can be summa- the along-shelf velocity under upwelling-favorable wind rized as (i) the generation of an intensified onshore conditions. Following the procedure of Zhang and transport on the downstream side of the canyon where Lentz (2017), solutions of phase speed for the first three most deep/slope water flows toward the continental CTW modes, matching the characteristic alongshore shelf (Klinck 1996; Allen and Durrieu de Madron 2009; scales seen on the downstream region, are 1.5, 0.7, and 2 Ramos-Musalem and Allen 2019), (ii) a cyclonic circu- 0.3 m s 1, respectively in our eastern boundary configu- lation within the canyon (Hickey 1995; Kämpf 2007), and rations. These phase speeds do not match the incoming 2 (iii) an onshore deflection of shelfbreak currents flowing shelf flow (about 20.14 m s 1) that interacts with the downstream due to the gain of vorticity as the flow is canyon. Thus, the increased wavelengths found over the stretched over the canyon (She and Klinck 2000; Allen downstream region (Figs. 3 and 8) would not be pri- and Durrieu de Madron 2009; Allen and Hickey 2010). marily controlled by an arrested CTW. Differently from

Unauthenticated | Downloaded 10/07/21 03:05 PM UTC JUNE 2020 S A L D Í AS AND ALLEN 1693 the study of Zhang and Lentz (2017), the frontal system of our experiments is not in quasi-steady state. Thus, the evolving meandering flow interacts with the canyon and induces fluctuations in the canyon response that may not allow the proper adjustment for the standing CTW to be formed, as in the configuration of Zhang and Lentz (2017). It is likely that the primary control on the frontal wavelengths is the increased Rossby radius of deformation (NH/f) as a result of the enhanced dense water pool from canyon-induced upwelling. In fact, the evolution of shelf stratification shows higher values on the downstream side of the canyon and in deeper shelves (not shown). This control would be consistent with the theory of frontal instabilities for which wavelength scales, to a large extent, on the order of the baroclinic Rossby radius of deformation (Cushman-Roisin and Beckers 2011). These frontal instabilities (;20 km) agree well with the second rapidly growing mode found by FIG. 13. Cross-canyon ratio (downstream/upstream) of cross- Barth (1994) for an eastern boundary. On the other shelf density difference (onshore–offshore), and difference in alongshore wavelengths (downstream minus upstream) as a func- hand, a more complicated mechanism is expected to im- tion of Burger number (Bu) for shallow, intermediate, and deep pact these wavelengths due to the partial influence of a shelf experiments with a canyon. Average values (and their stan- barotropic instability around the front (positive KmKe in dard deviations) are calculated for the last five days of experiments Fig. 11). The alongshore scales of mixed barotropic– when frontal instabilities are better developed. The Burger number baroclinic instabilities in a shelfbreak front has been is for the downstream shelf (NHs/fL), where N is the average stratification over the shelf, Hs is the depth next to the coast, f is shown to depend in part on the Burger number (Bu; e.g., the Coriolis parameter, and L is the shelf width. The cross-canyon Zhang and Gawarkiewicz 2015). Our canyon experi- ratio of cross-shelf density difference decreases with Bu whereas ments show a high dependence on the Burger number the difference in wavelengths increases with Bu. over the downstream side of the canyon (Fig. 13), where Bu increases with shelf depth configuration due to higher differences between the canyon and no-canyon cases are depth and slightly higher stratification. The difference in confined to the ageostrophic (Ageo.) and advection wavelengths increases with Burger number (larger dif- terms, which are enhanced and nearly balance each ferences on deeper shelves), whereas surface density ra- other around the canyon (Figs. 14h,l). Because the up- tios decreases with Burger number since the largest welling jet is primarily in thermal wind balance, the density differences between downstream and upstream Coriolis and pressure gradient terms are also shown to regions occur on shallower shelves (Fig. 13). The domi- highlight the impact of the canyon not only in disrupting nant terms of the depth-averaged cross-shore momentum this balance in the region above the canyon head equation are shown in Fig. 14 for the intermediate shelf but also its influence in decelerating the jet farther up- configurations. Here, the acceleration (Accel.) is princi- stream and accelerating it immediately downstream pally balanced by the sum of the horizontal advection and onshore of the canyon’s head (Figs. 14i,j). Here, (Adv.), Coriolis acceleration (Cor.), pressure gradient the negative ageostrophic term is due to the negative (PG), and surface (SS) and bottom (BS) stresses: Coriolis term overcoming the positive pressure gradient (Fig. 14k). Thus, there is an ageostrophic southward flow ›U U›U V›U 1›P t t 52 2 1 fV 2 1 s 2 b , associated with the Coriolis acceleration. Moreover, the ›t ›x ›y |{z} r ›x hr hr |{z} |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} |ffl{zffl}o |{z}o |{z}o zonal bottom stress is higher along the southern side of Accel. Cor. Adv. |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}PG SS BS the canyon (Fig. 14l) and reduced farther downstream in Ageo. comparison with the no-canyon case (Fig. 14f). This (14) confirms that the downstream side of the canyon is the principal area of near-bed upwelling of deep/slope water where U and V are the cross-shore and alongshore from the canyon with implications on the advection of depth-averaged velocity components, respectively; t is tracers onto the continental shelf (Hickey and Banas time; f is the Coriolis parameter; P is pressure; ro is a 2008; Connolly and Hickey 2014; Ramos-Musalem and reference density; ts and tb are surface and bottom Allen 2019). However, it plays a minor role in the overall stresses; and h is the water column depth. The largest zonal momentum balance. This dynamical analysis reaffirms

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FIG. 14. Dominant terms in the depth-averaged cross-shore momentum equation [Eq. (14)] by the end of day 25 for intermediate shelf experiments (g)–(l) with (Exp4) and (a)–(f) without (Exp3) a submarine canyon. The isobaths of 150, 200, 300, and 400 m are shown in black contours. The terms are denoted as acceleration (Accel), advection (Adv), Coriolis (Cor), pressure gradient (PG), ageostrophic (Ageo 5 Cor 1 PG), and bottom stress (BS). Advection and ageostrophic terms dominate both the dynamics of frontal instabilities and the circulation around the submarine canyon. The geostrophic upwelling jet decelerates (accelerates) over the upstream (downstream) region. the crucial importance of nonlinear terms allowing in- onshore/offshore displacement of the coastal upwelling tensified cross-shore exchanges by scale evolving frontal jet in more realistic conditions. The impact of submarine instabilities (e.g., Durski et al. 2007) or flow–topography canyons enhancing upwelling of deep waters over the interactions (e.g., Castelao and Barth 2006). It is still continental shelf has been well documented (e.g., Allen unclear how a time-dependent wind forcing would and Durrieu de Madron 2009; Connolly and Hickey change our results. Although our steady wind forcing 2014; Sobarzo et al. 2016; Ramos-Musalem and Allen sets a basis for future comparisons with more realistic 2019). This canyon-driven upwelling is mostly confined numerical experiments, we anticipate that considerable to subsurface and bottom depths of the shelf. The frontal differences in the circulation may occur since time- instabilities, however, increase the impact of the canyon dependent wind forcing produces unique characteris- at the surface (see Fig. 3). Thus, the combination of an tics such as the formation of a cyclonic eddy deep within unstable upwelling jet, promoting the development of the canyon (Allen and Hickey 2010), transient pools of frontal instabilities, and a submarine canyon leads to dense water over the shelf depending on the strength enhanced density (and implied nutrients and tracers) to and periodicity of the wind stress (Kämpf 2006), and the top 20 m of the water column (Fig. 3), which may even downwelling currents under wind relaxation events have a significant impact on the productivity and the (Hickey 1997). We also plan to inspect, in future studies, budget of tracers in the upper layer of the continental the consequences of spatially varying wind stress. A shelf. Upwelling waters are also characterized by low pH coastal band of intense wind stress curl is common in and elevated CO2 partial pressure (e.g., Torres et al. eastern boundary systems (e.g., Münchow 2000; Capet 2011; Evans et al. 2015). Thus, under enhanced upwell- et al. 2004; Aguirre et al. 2014), which can force, in a ing conditions (i.e., as result of the combined effect of large extent, the offshore displacement of the upwelling frontal instabilities over a canyon) increased CO2 out- jet (Samelson et al. 2002; Castelao and Barth 2007; gassing occurs in regions characterized by reduced bio-

Aguirre et al. 2012). Thus, a submarine canyon and the logical efﬁciency (uptake of CO2 is low compared to the wind stress curl ﬁeld can be acting oppositely on the content being upwelled) such as in the central California

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FIG. 15. Schematics of coastal upwelling in an eastern boundary (a) with and (b) without the influence of a submarine canyon. The submarine canyon influences coastal upwelling in three main aspects: (i) the inshore turn and acceleration of the upwelling jet, (ii) the generation of a downwelling area farther downstream, which is followed by a high pool of enhanced upwelled water, and (iii) the break of wavelengths in the frontal instabilities, being longer downstream of the canyon. and the southern Canary current systems (Lachkar and with isopycnals tilted offshore (like a typical buoyancy- Gruber 2013). Note that this should also occur with driven flow) and a mesoscale flow that meanders over a other greenhouse gases (N2O, CH4), which are released canyon, which is a completely different scenario than the at high rates in eastern ocean boundaries (Kock et al. one during eastern boundary coastal upwelling. Here, a 2008; Florez-Leiva et al. 2013). Enhanced upwelling set of process-oriented numerical experiments, consid- also has biological consequences near the bottom since ering three contrasting shelf depth/slope cases, are used mass die-offs of benthic organisms have been linked to to study the main effects that a submarine canyon has on upwelling-driven hypoxia/anoxia over the shelf (Grantham the circulation and cross-shore exchanges in a coastal et al. 2004; Hernández-Miranda et al. 2012). ocean model of coastal upwelling characterized by the development of frontal instabilities. Our results show that, in the absence of a canyon, coastal upwelling forms a 5. Summary and conclusions surface front over the shelf, which drives a baroclinic jet Although submarine canyons and upwelling frontal flowing downstream (Fig. 15a). Finite-scale baroclinic instabilities (in the form of filaments and eddies) are instabilities are formed and evolve around the front. ubiquitous features in eastern boundary current sys- Cross-shore exchanges are enhanced by these frontal in- tems, process-oriented studies of the circulation and stabilities, which promote spatial and temporal variability exchanges have, in general, evaluated their impacts in the net offshore transport (Fig. 12). They can also separately. The few studies taking into consideration a produce net onshore transport at times, however, these canyon-front interaction were set and focused on a front episodes are insignificant in the accumulated transport

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